The Theory of Nilpotent Groups
The Theory of Nilpotent Groups

Author: Anthony E. Clement

Publisher: Birkhäuser

Published: 2017-11-18

Total Pages: 318

ISBN-13: 3319662139

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This monograph presents both classical and recent results in the theory of nilpotent groups and provides a self-contained, comprehensive reference on the topic. While the theorems and proofs included can be found throughout the existing literature, this is the first book to collect them in a single volume. Details omitted from the original sources, along with additional computations and explanations, have been added to foster a stronger understanding of the theory of nilpotent groups and the techniques commonly used to study them. Topics discussed include collection processes, normal forms and embeddings, isolators, extraction of roots, P-localization, dimension subgroups and Lie algebras, decision problems, and nilpotent groups of automorphisms. Requiring only a strong undergraduate or beginning graduate background in algebra, graduate students and researchers in mathematics will find The Theory of Nilpotent Groups to be a valuable resource.

Localization of Nilpotent Groups and Spaces
Localization of Nilpotent Groups and Spaces

Author: Peter Hilton

Publisher: Elsevier

Published: 2016-06-03

Total Pages: 167

ISBN-13: 1483258742

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North-Holland Mathematics Studies, 15: Localization of Nilpotent Groups and Spaces focuses on the application of localization methods to nilpotent groups and spaces. The book first discusses the localization of nilpotent groups, including localization theory of nilpotent groups, properties of localization in N, further properties of localization, actions of a nilpotent group on an abelian group, and generalized Serre classes of groups. The book then examines homotopy types, as well as mixing of homotopy types, localizing H-spaces, main (pullback) theorem, quasifinite nilpotent spaces, localization of nilpotent complexes, and nilpotent spaces. The manuscript takes a look at the applications of localization theory, including genus and H-spaces, finite H-spaces, and non-cancellation phenomena. The publication is a vital source of data for mathematicians and researchers interested in the localization of nilpotent groups and spaces.

Nilpotent Groups and their Automorphisms
Nilpotent Groups and their Automorphisms

Author: Evgenii I. Khukhro

Publisher: Walter de Gruyter

Published: 2011-04-20

Total Pages: 269

ISBN-13: 3110846217

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The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany

Lecture Notes on Nil-Theta Functions
Lecture Notes on Nil-Theta Functions

Author: Louis Auslander

Publisher: American Mathematical Soc.

Published: 1977

Total Pages: 106

ISBN-13: 0821816845

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Consists of three chapters covering the following topics: foundations, bilinear forms and presentations of certain 2-step nilpotent Lie groups, discrete subgroups of the Heisenberg group, the automorphism group of the Heisenberg group, fundamental unitary representations of the Heisenberg group, and the Fourier transform and the Weil-Brezin map.

Lectures on Lie Algebras
Lectures on Lie Algebras

Author: J. A. Bahturin

Publisher: Walter de Gruyter GmbH & Co KG

Published: 1978-12-31

Total Pages: 136

ISBN-13: 3112761715

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No detailed description available for "Lectures on Lie Algebras".

Lower Central and Dimension Series of Groups
Lower Central and Dimension Series of Groups

Author: Roman Mikhailov

Publisher: Springer Science & Business Media

Published: 2009

Total Pages: 367

ISBN-13: 3540858172

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A fundamental object of study in group theory is the lower central series of groups. Understanding its relationship with the dimension series is a challenging task. This monograph presents an exposition of different methods for investigating this relationship.

Elementary Theory of Groups and Group Rings, and Related Topics
Elementary Theory of Groups and Group Rings, and Related Topics

Author: Paul Baginski

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2020-02-10

Total Pages: 274

ISBN-13: 311063838X

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This proceedings volume documents the contributions presented at the conference held at Fairfield University and at the Graduate Center, CUNY in 2018 celebrating the New York Group Theory Seminar, in memoriam Gilbert Baumslag, and to honor Benjamin Fine and Anthony Gaglione. It includes several expert contributions by leading figures in the group theory community and provides a valuable source of information on recent research developments.